Electron-Phonon Coupling from Ab Initio Linear-Response Theory within the GW Method: Correlation-Enhanced...

We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the GW method. This approach, named GW perturbation theory (GWPT), is applied to calculate the electron-phonon (e-ph) interactions with the full inclusion of the GW nonlocal, energy-dependent self-energy effects, going beyond density-functional perturbation theory. Avoiding limitations of the frozen-phonon technique, GWPT gives access to e-ph matrix elements at the GW level for all phonons and scattering processes, and the computational cost scales linearly with the number of phonon modes (wave vectors and branches) investigated. We demonstrate the capabilities of GWPT by studying the e-ph coupling and superconductivity in Ba_{0.6}K_{0.4}BiO_{3}. We show that many-electron correlations significantly enhance the e-ph interactions for states near the Fermi surface, and explain the observed high superconductivity transition temperature of Ba_{0.6}K_{0.4}BiO_{3} as well as its doping dependence.